Question

If one root of equation $x^2+ax+12=0$ is $4$ while the equation $x^2+ax+b=0$ has equal roots, then the value of $b$ is

• A. $\frac{4}{49}$
• B. $\frac{49}{4}$
• C. $\frac{7}{4}$
• D. $\frac{4}{7}$

Answer 1

Answer: (B)

Since, $4$ is a root of $x^2+ax+12=0$
$\therefore 16+4a+12=0$
$\Rightarrow a=-7$
Let the roots of the equation $x^2+ax+b=0$ be $\alpha$ and $\alpha$.
$\therefore 2\alpha =-a$
$\Rightarrow \alpha =\frac{7}{2}$
and $\alpha \cdot \alpha =b$
$\Rightarrow {\left(\frac{7}{2}\right)}^2=b$
$\Rightarrow b=\frac{49}{4}$